ANS:C - parabolloid

When a circular slab is subjected to external loading, its deflection pattern depends on various factors such as the loading conditions, support conditions, and material properties. However, the deflection pattern typically does not form a perfect semi-hemisphere, ellipsoid, or paraboloid. Here's a brief explanation of why:

1. Semi-hemisphere: A semi-hemisphere is a half-sphere shape, resembling the top half of a sphere. While a circular slab may experience some degree of doming or bulging under loading, the deflection is unlikely to form a perfect semi-hemisphere shape, especially if the slab is relatively thin and flexible.
2. Ellipsoid: An ellipsoid is a three-dimensional geometric shape resembling a stretched or compressed sphere. While it's possible for a circular slab to deform into a non-uniform shape resembling an ellipsoid under certain loading conditions, this is less common and typically occurs in highly non-linear or complex structural behavior, which is not typical for circular slabs.
3. Paraboloid: A paraboloid is a three-dimensional surface formed by revolving a parabola around its axis. While paraboloids can arise in certain structural configurations, such as hyperbolic paraboloids in shell structures, it's not typical for a circular slab subjected to external loading to deform into a perfect paraboloid shape.

Instead, the deflection pattern of a circular slab under external loading is more likely to exhibit a combination of bending, shear, and membrane effects, resulting in a complex deformation pattern that may not conform to simple geometric shapes like those mentioned above. Therefore, the correct answer is: None of these.None of these. The deflection pattern of a circular slab under external loading is more accurately described as a combination of various deformation modes rather than a perfect semi-hemisphere, ellipsoid, or paraboloid shape.